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Proposal for an Experiment to Test the Guidance of a Wave Component within the de Broglie–Bohm Theory

David DHUGUES

Published Jun 27, 2026• 0 citations
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Abstract

This paper proposes a double-slit experiment designed to test a hypothetical extension ofthe de Broglie–Bohm theory. The hypothesis investigated is that a component associated withthe wave function, referred to here as a “wave component”, could be guided by external opticaldevices independently of the photon itself. This contribution is modeled as a modification ofthe wave-function input entering Bohm’s guiding equation. To the best of my knowledge, noexperimental setup explicitly investigates a mechanism of this type involving the capture andreinjection of a wave-function-related contribution through an external optical system.

DOI
10.5281/zenodo.20963959

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This paper proposes a double-slit experiment designed to test a hypothetical extension ofthe de Broglie–Bohm theory. The hypothesis investigated is that a component associated withthe wave function, referred to here as a “wave component”, could be guided by external opticaldevices independently of the photon itself. This contribution is modeled as a modification ofthe wave-function input entering Bohm’s guiding equation. To the best of my knowledge, noexperimental setup explicitly investigates a mechanism of this type involving the capture andreinjection of a wave-function-related contribution through an external optical system.
We reply to Akhavan and Golshani's comment on our double-slit experiment addressed to test standard quantum mechanics versus de Broglie–Bohm theory. We show that their results, albeit representing a relevant contribution to the discussion on the realizability of a test of de Broglie–Bohm theory, do not allow us to draw any conclusion about our experiment since their wavefunction does not describe well the photon states produced by our set-up. On the other hand, we give arguments of why our experiment can be considered a good realization of the theoretical proposal of Ghose (1999 Foundations of Quantum Theory and Quantum Optics ed S M Roy), Ghose et al (2001 Phys. Lett. A 290 205) and Golshani and Akhavan ( 2001 J. Phys. A: Math. Gen. 34 5259 ).
I will try to interest you in the de Broglie–Bohm version of non-relativistic quantum mechanics. It is, in my opinion, very instructive. It is experimentally equivalent to the usual version insofar as the latter is unambiguous. But it does not require, in its very formulation, a vague division of the world into ‘system’ and ‘apparatus,’ nor of history into ‘measurement’ and ‘nonmeasurement.’ So it applies to the world at large, and not just to idealized laboratory procedures. Indeed the de Broglie–Bohm theory is sharp where the usual one is fuzzy, and general where the usual one is special. This is not a systematic exposition, but only an illustration of the ideas with a particularly nice example, and then some remarks on the role of the density matrix – in tribute to the title of this conference. No one more eloquently than John A. Wheeler has presented the delayed-choice double slit experiment. A pulsed particle source S (see Fig. 1) is so feeble that not more than one particle is emitted per pulse. The associated wave pulse B falls on a screen with slits 1 and 2. The transmitted pulses B′ are focussed by off-centred lenses into intersecting plane wave trains which fall finally on particle counters C 1 and C 2 – unless a photographic plate P is pushed into the region where the two wave trains interpenetrate. The decision, to interpose the plate or not, is made only after the pulse has passed the slits.
The double slit experiment is a relatively simple physical test that can be useful for demonstrating the corpuscular-wave dualism of light and matter, which is the supreme mystery of the whole quantum physics. A particular riddle here is especially the mechanism responsible for the formation of a interference pattern in a situation when single quantum objects pass through the experimental setup. In the article the main idea of the experiment is discussed and two possible explanations of its results are briefly shortly presented: the view of the Copenhagen school and the de Broglie-Bohm’s pilot wave theory.